%I M1879 #21 May 01 2014 02:40:01

%S 0,0,0,0,0,1,2,8,48,450,5751,90553,1612905,31297357,652159389,

%T 14499780660,342646718608

%N Number of connected trivalent graphs with 2n nodes and girth exactly 5.

%D CRC Handbook of Combinatorial Designs, 1996, p. 647.

%D Gordon Royle, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>

%F a(n) = A014372(n) - A014374(n).

%Y Connected k-regular simple graphs with girth exactly 5: this sequence (k=3), A184945 (k=4), A184955 (k=5).

%Y Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); specified g: A006923 (g=3), A006924 (g=4), this sequence

%Y (g=5), A006926 (g=6), A006927 (g=7).

%Y Connected 3-regular simple graphs with girth at least g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

%K nonn,hard,more

%O 0,7

%A _N. J. A. Sloane_.

%E Definition corrected to include "connected", and "girth at least 5" minus "girth at least 6" formula provided by _Jason Kimberley_, Dec 12 2009